Solution 1:

This is a strange theory that is provably wrong. It is easy to trace "I am working" back to determine that it has not developed from "I am at working", and it is obvious that the rheinische Verlaufsform is different from the English Present Progressive in other ways, not just the preposition. For starters, it uses the nominalized bare infinitive, and it uses it with a definite article. So the English counterpart would really be "I am at the work", where work is a bare infinitive. Does not compute, sorry.

Edit: oh, and the German equivalent of this English -ing is actually -end. So it would have to be "ich bin arbeitend" in German, or something along those lines. Not "ich bin am Arbeiten".

Solution 2:

After some research I came across this remarkable academic document "On the progression of the progressive in early Modern English - icame": Please, read especially page 7, I think this is the actual puzzle piece we're looking for! Here some excerpts:

"... There seems to be pretty general agreement that at least as far as form is concerned it derives most directly from a construction in Old English, with parallels in many other early Germanic languages, which also consisted of a combination of a BE verb and a present participle, in Old English generally taken the ending -ende ... this construction was more common in translations from Latin, especially of complex Latin verb forms, than in original Old English texts ..." => e.g.: æt scip wæs ealne weg yrnende under segle. (that ship was all the way running under sail.)

Further quoting:

"... In Middle English two things happened: the BE plus present participle construction, never particularly frequent in Old English, became even less frequent, and the form of the present participle changed, from taking the ending -ende to taking -ing, to coincide with the nominal verb form known as the gerund, now regularly also ending in -ing. This meant not only that the construction of BE plus present participle became formally more similar to the progressive construction we are familiar with today; it also meant that the Middle English construction of BE plus present participle became more similar to another construction that occurred in Old and Middle English, with BE followed by a preposition, often on, plus the gerund, as in Old English ..." => ZyrstandæZ ic wæs on huntunZe (Here huntunZe is the nominal verb form, the gerund, corresponding to Modern English hunting, and so it means Yesterday I was hunting.)

And finally:

"... In Middle English similar constructions began to be common with just a light a before the main verb, as in ‘He was a-hunting.’, generally seen as a remnant of the full preposition. If the preposition was not only reduced but dropped altogether, there was no longer any formal difference between the two constructions: that with BE followed by the present participle, and that with BE followed by the gerund, now without any intervening preposition. At about the same time that this levelling of the difference between the two constructions became widespread, i.e. roughly at the transition from Middle to Modern English at around A.D. 1500, the combined construction consisting of BE plus an -ing-form seems to have started to increase quite drastically in frequency. ..."

Solution 3:

I was just about to ask this question and saw that you already asked it. I only have hypotheses.

When I first read the terminology for the progressive/continuous aspect in English, it was be + gerund. That struck me as strange, since it seems that when you say “The teacher is talking,” the word talking modifies the teacher as adjectives normally modify nouns, as in “The teacher is tall” and “The teacher talking right now is Mrs. Lewis.” So, the -ing word seems to be functioning as a present participle. Indeed, today it’s more popular to call it a present participle.

Why two grammatical terms?

Considering that the gerund and the present participle always have the same form in English, where did people get the idea to call it by two names? The obvious suspect is people trying to understand English grammar in terms of Latin grammar—or perhaps by analogy with Romance languages. Italian has a present progressive and distinct forms for the gerund and present participle. And indeed, in Italian you say L’insegnante sta parlando (with the gerund), not L’insegnante sta parlante (present participle). But in English, the two forms are the same, so maybe the very question of which term to use for the -ing word in a progressive tense is pointless hair-splitting, resulting only from trying to force-fit English grammar terminology to foreign grammatical distinctions. Better to just call it “the -ing word” and be done with it.

On the other hand, just because two words have the same form doesn't mean they serve the same grammatical function. You modify a present participle with an adverb (“loudly talking") but you modify a gerund with an adjective (“loud talking”). You modify a verb in a progressive tense with an adverb (“The teacher is talking loudly”), so that would seem to seal the case for having two grammatical terms and for saying that the -ing word in progressive tenses is a present participle.

More grammatical functions

But wait! After looking at how the gerund and present participle are used in Italian, it’s clear that there are still more, decidedly distinct grammatical functions here. Consider the following:

A rolling stone gathers no moss.

A grinding stone is very heavy.

Rolling refers to the time when the stone is failing to gather moss. This is what the gerund means in Italian outside of progressive tenses: something happening while the main verb is happening or in connection with the main verb. While the stone is rolling and because the stone is rolling, it gathers no moss.

Grinding is an adjective describing the kind of stone. This is what the present participle means in Italian: it really is a way of converting a verb into an adjective, not a way to predicate something of a noun (the essential function of verbs).

Notice that in the present progressive tense, in both English and Italian, the verb predicates some action of the subject right now. This seems like a reasonable argument for saying that the present progressive in English is formed from be + gerund, not be + present participle, though of course the argument for the latter is pretty strong, too.

More grammatical restrictions

And can you really not modify a gerund with an adverb? We say “Loud talking is annoying” but also “Talking loudly is annoying.” “Loudly talking is annoying” is strange but maybe grammatical, and “Talking loud is annoying” is decidedly ungrammatical. Yet talking is clearly a noun in every sentence, and therefore seemingly a gerund.

Conclusion #1

Now consider:

My car is running.

Interpreted as a gerund, that would mean that your car’s engine is on right now. Interpreted as a present participle, that would mean that you have a running car right now, that is, a functional car.

So, my current thinking (tonight) is that the progressive tenses are made with be + gerund after all, contra my initial disbelief. Only, this is a gerund functioning as a verb, not a noun.

Another test of this hypothesis:

The children are describing talking with you at Chuck E. Cheese.

The children are describing talking robots at Chuck E. Cheese.

In the first sentence, talking is a gerund. In the second, talking is a present participle. And so describing is a gerund in both: it's really part of the verb, saying what the children are doing, not an adjective modifying children.

Conclusion #2

On the other hand, the fact that the gerund also functions as a noun (the Romance gerunds can’t do that) and the weird quasi-rules about where you need to put adjectives and adverbs make me think that the -ing form of a verb is just the usual English grammatical mish-mash: it serves many different roles, by various, sometimes conflicting, analogies with a variety of familiar constructions that serve as precedents, sometimes simultaneously. An ideal terminology might have to sort out the roles independently of the syntax, and allow a single -ing to serve more than one role at once.

There are two roles like Romance-language gerunds (present progressive and “something happening in connection with something else that’s happening”), there’s a role as a noun that works almost the same as an infinitive (also called “gerund”), there’s a role as an adjective unrelated to the time of the main verb, and maybe there are more. In a sentence like:

I am imagining playing the piano.

you could say that playing is a noun, the object of imagining, or you could say that playing is a gerund asserting an action that’s connected with imagining, or you could say that playing is a subordinate gerund, or you could even say that imagining playing is a compound present progressive verb. Just as with the many interpretations of quantum mechanics that are consistent with all observations, the language doesn’t provide evidence to say that one of these theories is right and the others are wrong.

Please, someone explain to me why this is wrong, either in a comment or another answer!

Solution 4:

Not only does your reconstruction of the English progressive as from a nominal construction with "at" make sense, it's still true! George Lakoff pointed out some years ago, that we can pronominalize the -ing progressive form with "it" provided we use "at":

She was working in her garden at 4, and two hours later, she was still at it.

At what? one might ask. At working in her garden, evidently. So since it is object of "at", it must be a nominal, hence a gerund rather than a participle.